The two major problems with flash pictures are 'bleaching' where the face is too pale because the flash is too close, and 'red-eye', where the retina of the eye has reflected the flash. To avoid the first, check your camera handbook for flash distances.
When taking a portrait by flash, ask your subject not to look directly at the camera or, better still, to look first at a bright light before looking back at the camera (the light closes the pupil and prevents the reflection).
You can also reduce red-eye by increasing the light in the room, by switching on more lights or by drawing back curtains.
These problems are unlikely to arise with single-lens reflex cameras where the flash gun is mounted on the camera's 'hot shoe'. With a swivel-head gun you can 'bounce' the flash off the ceiling, or fit a diffuser lens to soften the light.